Thursday, December 27, 2007

Trading vs. Investing

Snork Maiden commented on Tuesday's post "If we earned so much more from passive investments and long-term capital gains than from trading, maybe we should put more into those kind of investments and less into active trading?".

Well it's not so simple to make that judgment. We only have 6% of net worth allocated to trading vs. 61% allocated to other non-retirement assets. So the $31,691 we earned from longer term investments and cash represents a lower rate of return than the $9,294 we earned from trading. In fact the non-trading rate of return on assets (not equity) was just 11.5% while the trading rate of return was 34.9%. On the other hand, much more risk was experienced in earning the trading income. The Sharpe Ratio in trading for the twelve months of 2007 was about 0.49 while for all non-retirement accounts (including trading) it was 0.90 - in other words relative to volatility excess returns were around twice as high. Based on this, if unlimited leverage at reasonable interest rates was available it would be optimal to lever up the non-trading return instead of trading. On the other hand, the correlation between trading and total non-retirement investment returns is just 0.34. Therefore, it would make sense to have a diversified portfolio that included long-term investments and trading. Depending on preferences, probably the optimal allocation to trading would quite small and some leverage should be used in investing. And that is exactly what we are doing.

This argument is pretty obvious I think if you are familiar with "modern portfolio theory". This graphic illustrates this argument:

The y-axis is the rate of return - 34% for trading and 11% for investing. The x-axis gives the standard deviation of returns, 13% and 70% respectively. The curved black line is the "efficient frontier" - portfolios that allocate varying amounts to trading and investing. The shape of the frontier here is purely illustrative. If the investor has to put all their money into a mixture of investments and trading and can't allocate any to cash and also can't borrow any money then they are going to be at some point on this frontier. With 100% in trading they will be at the point marked trading and with 100% in investing at the point marked investing. Points to the left of investing or right of trading involve shorting one of the two asset classes. The points in between are more interesting for practical cases. Because of the low correlation between investing and trading allocating some money to trading at first raises returns by relatively more than it increases risk - in other words the efficient frontier is convex (up). As we allocate more and more to trading risk increases relatively fast compared to return. Where the optimal point is depends on the investor's preferences. More risk-averse investors will choose more investment and less trading.

If we can also allocate money to cash, the picture is different. Now, it is optimal for all investors to choose the portfolio marked with the green spot for their risky investments and combine this portfolio with cash investments along the green line. If they allocate 100% to cash they receive the risk-free rate (RF) but have zero risk - they are at the point marked RF on the y-axis. Again, where on the green line you invest depends on your level of risk-aversion. By the way, this simple investment theory says that the typical advice to invest more in bonds as you age or have greater risk intolerance makes no sense, unless we are talking about 90 day government bonds which are cash equivalents. All investors should have the same percentage portfolio allocations for their risky investments but different amounts of cash.

If we can borrow money - margin loans, mortgages etc - the picture changes again. Usually the rate we can borrow at is higher than the rate we can lend at and the optimal portfolio is marked by the red point where the red line is tangent to the efficient frontier. The red line starts out at the borrowing rate (BR) which is higher than the risk free rate. This means that if we are thinking about borrowing to invest it is optimal to choose a riskier portfolio to invest in. There is a quantum leap in thinking about risk between leveraged and non-leveraged investors. By borrowing money we have access to return-risk combinations along the solid red line. The more we borrow the higher the return, but the higher the risk. Still borrowing allows us to get higher returns for less risk than if we simply allocated more money to the riskier asset - trading. Again, which point on the line is optimal depends on preferences. We aren't borrowing a lot so we are still relatively risk-averse compared to a more leveraged investor.

There are three counterintuitive results here - examples of what makes economic theory interesting - everyone should have the same allocations to different asset classes once they decide how much to invest in risky assets - but if we borrow to invest we should go for a riskier underlying portfolio - and borrowing to invest is safer than trying to maximize returns by allocating more to high risk investments. All of these go against what most people would think is common sense on investing.

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